Ataullah Khogyani, a spokesman for the provincial governor, said the blast damaged the security facility and several other buildings.
Several of the injured police officers were listed critical condition, officials said.
In Nangarhar province, at least seven people were injured when an explosives-packed motorcycle was detonated near an education facility, Khaama Press reported.
A security official said a university student believed to be the motorcycle's owner was arrested.
No one initially claimed responsibility for either attack, Khaama Press said.